A particle travels along the x-axis such that its velocity is given by v(t)=t^(1.1)-2-5cos(3t). What is the acceleration of the particle at time t=1 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

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A particle travels along the  x-axis such that its velocity is given by  v(t)=t^(1.1)-2-5cos(3t). What is the acceleration of the particle at time  t=1 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

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Differentiate Velocity Function: To find the acceleration of the particle at time t=1, we need to differentiate the velocity function v(t) with respect to time t to get the acceleration function a(t). The velocity function is v(t)=t^(1.1)-2-5cos(3t).Combine Derivatives: Differentiate each term of the velocity function separately. The derivative of t^(1.1) with respect to t is 1.1*t^(0.1). The derivative of a constant is 0, so the derivative of -2 is 0. The derivative of -5cos(3t) with respect to t is 15sin(3t) because the derivative of cos(u) is -sin(u) and we apply the chain rule with an inner function of 3t, which gives us an additional factor of 3.Evaluate Acceleration at t=1: Combine the derivatives to get the acceleration function a(t) which is a(t)=1.1*t^(0.1)+15sin(3t).Calculate a(1): Evaluate the acceleration function at t=1 to find the acceleration at that time. So, a(1)=1.1*1^(0.1)+15sin(3*1).Perform Calculation: Calculate the value of a(1). Since 1 to any power is 1, we have 1.1*1^(0.1) = 1.1. The sine of 3 radians can be calculated using a calculator. sin(3) is approximately 0.1411. So, 15sin(3) is approximately 15*0.1411.Add Values: Perform the calculation: a(1) = 1.1 + 15*0.1411. Using a calculator, we find that 15*0.1411 is approximately 2.1165. So, a(1) = 1.1 + 2.1165.Round Final Answer: Add the two values to get the final acceleration at t=1. a(1) = 1.1 + 2.1165 = 3.2165.Round the final answer to the nearest thousandth as instructed. The rounded value of a(1) is 3.217.

A particle travels along the $x$ -axis such that its velocity is given by $v(t)=t^{1.1}-2-5 \cos (3 t)$ . What is the acceleration of the particle at time $t=1$ ? You may use a calculator and round your answer to the nearest thousandth. $\newline$ Answer:

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